Where should the center of mass be on a stick to maximize rotation when pushed?

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jbriggs444 said:
The original question is not well enough posed to have a definite answer. But yes, for a reasonable understanding of the intended question, the answer is "the middle".
PeroK put it way better than I did:When you give an impulse to one end of the rod, the COM moves forward and the object rotates around the COM. The initial velocity of the other end if the rod is the sum of the forward velocity of the COM and a backwards velocity from the rotation.

Question: what mass distribution will result in the other end of the rod initially moving backwards from its starting position with the greatest speed?
 
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Erunanethiel said:
Question: what mass distribution will result in the other end of the rod initially moving backwards from its starting position with the greatest speed?
Answer: undefined. There is no optimum. The distribution with all of the mass exactly in the center results in an undefined speed and, accordingly, is ineligible.
 
jbriggs444 said:
Answer: undefined. There is no optimum. The distribution with all of the mass exactly in the center results in an undefined speed and, accordingly, is ineligible.
Do you mean that the location of center of mass does not matter for this, the only thing that does is how "centralized" the mass is to CoM, irrespective of it's location. In short: Make every where that is not CoM make as light as possible.

Correct?
 
Erunanethiel said:
Do you mean that the location of center of mass does not matter for this, the only thing that does is how "centralized" the mass is to CoM, irrespective of it's location. In short: Make every where that is not CoM make as light as possible.
The location of the center of mass relative to the ends matters. But so does the degree to which the mass is centralized. Both are relevant. One can even write an equation.

Try it. Apply an impulse "p" at right angles to one end of a rod of length "l" and mass "m" with center of mass offset "r" from the end where the impulse will be applied. If the rod has a moment of inertia "I", what speed will the other end have as a result?

Edit: Take it a step at a time. For instance, what rotation rate will result from the applied impulse?
 
jbriggs444 said:
Answer: undefined. There is no optimum. The distribution with all of the mass exactly in the center results in an undefined speed and, accordingly, is ineligible.
Well, not that the other bits have no mass, they are as I said made as light as possible
 
jbriggs444 said:
The location of the center of mass relative to the ends matters. But so does the degree to which the mass is centralized. Both are relevant. One can even write an equation.

Try it. Apply an impulse "p" at right angles to one end of a rod of length "l" and mass "m" with center of mass offset "r" from the end where the impulse will be applied. If the rod has a moment of inertia "I", what speed will the other end have as a result?

Edit: Take it a step at a time. For instance, what rotation rate will result from the applied impulse?
If the location of the center of mass relative to the ends matters, would the optimum position be in the middle, or closer to the side which the force is applied?
 
Erunanethiel said:
If the location of the center of mass relative to the ends matters, would the optimum position be in the middle, or closer to the side which the force is applied?
Sorry, you are going to have to put some effort of your own into this problem. Until you do, I'm out.